4
$\begingroup$

Find the next number in this sequence:

2, 4, 8, 13, 20, 29, 41, ?

EXTENSION: Find the number for the nth term in the sequence (in terms of n).

Hint:

Fibonacci+Triangle

$\endgroup$
5
  • $\begingroup$ mathworld.wolfram.com/TribonacciNumber.html $\endgroup$
    – Duck
    Sep 9, 2018 at 2:33
  • $\begingroup$ The hint has nothing to do with that. $\endgroup$ Sep 9, 2018 at 2:34
  • $\begingroup$ Ok, just checking $\endgroup$
    – Duck
    Sep 9, 2018 at 2:35
  • $\begingroup$ And I changed it to make it more obvious. $\endgroup$ Sep 9, 2018 at 2:37
  • 1
    $\begingroup$ OEIS found this but I don't think that is what you had in mind $\endgroup$ Sep 9, 2018 at 2:45

2 Answers 2

7
$\begingroup$

I think the answer is

57

Solution for the extension: (Thanks @PerpetualJ for MathJax)

$$Fi. Δ.$$ $$1 + 1 = 2$$ $$1 + 3 = 4$$ $$2 + 6 = 8$$ $$3 + 10 = 13$$ $$5 + 15 = 20$$ $$8 + 21 = 29$$ $$13 + 28 = 41$$ $$21 + 36 = 57 \leftarrow (Next Term)$$

Round off to the nearest integer.
$Fi(n) = round\biggl(\frac{(-\frac{1}{\phi})^n}{\sqrt{5}}\biggr)$
$\Delta(n) = \frac{n(n + 1)}{2}$
$\int(n) = Fi(n) + \Delta(n) = round\biggl(\frac{(-\frac{1}{\phi})^n}{\sqrt{5}}\biggr) + \frac{n(n + 1)}{2}$

$\endgroup$
1
  • 1
    $\begingroup$ Yes, good job!! $\endgroup$ Sep 9, 2018 at 7:00
12
$\begingroup$

The next number is

$34$

The formula is

$2^n - \dfrac{(n-1)(n-2)(n-3)}2$

$\endgroup$
1
  • $\begingroup$ I'm thinking of a different formula and I realized this worked as well so I'll edit the question. $\endgroup$ Sep 9, 2018 at 2:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.